globalList = []
class MyList:
    def __init__(self):
        self._myList = [1, 2, 3]
    @property
    def myList(self):
        return self._myList + globalList
    @myList.setter
    def myList(self, val):
        self._myList = val
mL1 = MyList()
print("myList: ", mL1.myList)
mL1.myList.append(4)
print("after appending a 4, myList: ", mL1.myList)
mL1.myList.extend([5,6,"eight","IX"])
print("after extend, myList: ", mL1.myList)
Result:
myList:  [1, 2, 3]
after appending a 4, myList:  [1, 2, 3]
after extend, myList:  [1, 2, 3]
The problem I am facing is that mL1.myList.append(4) and mL1.myList.extend([5,6,"eight","IX"]) do not modify the _myList attribute in the mL1 object. How could I do to resolve the problem?
I define a method append() and a method extend() for the class object. It respectively appends to member myList and extends member myList.
global globalList  
globalList = []
class MyList():
    def __init__(self):
        self._myList = [1, 2, 3]
    @property
    def myList(self):
        return self._myList + globalList
    @myList.setter
    def myList(self, val):
        self._myList = val
    def append(self, val):
        self.myList = self.myList + [val]
        return self.myList  
    def extend(self, val):
        return self.myList.extend(val)
mL1 = MyList()
print("myList: ", mL1.myList)
mL1.append(4)
print("after appending a 4, myList: ", mL1.myList)
mL1.myList.extend([5,6,"eight","IX"])
print("after extend, myList: ", mL1.myList)
result is
>>> 
('myList: ', [1, 2, 3])
('after appending a 4, myList: ', [1, 2, 3, 4])
('after extend, myList: ', [1, 2, 3, 4, 5, 6, 'eight', 'IX'])
                        I would subclass list and override a few methods:
import itertools
class ExtendedList(list):
    def __init__(self, other=None):
        self.other = other or []
    def __len__(self):
        return list.__len__(self) + len(self.other)
    def __iter__(self):
        return itertools.chain(list.__iter__(self), iter(self.other))
    def __getitem__(self, index):
        l = list.__len__(self)
        if index > l:
            return self.other[index - l]
        else:
            return list.__getitem__(self, index)
It should work with just about everything:
In [9]: x = ExtendedList([1, 2, 3])
In [10]: x
Out[10]: [1, 2, 3]
In [11]: x.append(9)
In [12]: x
Out[12]: [9, 1, 2, 3]
In [13]: x.extend([19, 20])
In [14]: x
Out[14]: [9, 19, 20, 1, 2, 3]
In [15]: sum(x)
Out[15]: 54
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